<div id="principal">
<p><strong>Emilio Porcu</strong> -  <a href=http://www.stochastik.math.uni-goettingen.de">http://www.stochastik.math.uni-goettingen.de</a> </p>
<p>Universidad de Valparaiso, Valparaiso, Chile</p>
</font>




<ul style="text-align: justify;">

<li><font face="Arial" size="2" color="#000000">
<strong>Title:</strong>
</font>
</li>
<p>Analysis of natural processes evolving temporally over the sphere of the Earth</p>

<li><font face="Arial" size="2" color="#000000">
<strong>Abstract:</strong>
</font>
</li>
<p>This talk combines some general methodology in order to obtain new classes of matrix-valued correlation functions, associated to multivariate Gaussian random fields, that allow for two important properties: (i) each component of the matrix-valued function has compact support and the ranges may vary among the components, and (ii) the overall differentiability at the origin can be varied. Our results are the analogue of Wendland functions for univariate random fields. We illustrate our models through both a simulation study and an application to a North American bivariate dataset of precipitation and temperature. Since, for this dataset, as well as for others, the empirical covariances exhibit a hole effect, we also extend the Turning Bands operator to matrix valued covariance functions to obtain matrix-valued covariance models with negative correlations. Finally, we show that convolution arguments are feasible in one dimension, prohibitive in two dimensions and feasible, but pointless, in three dimensions. We also present an approach based on splines.</p>
</div>
